Derived equivalences of self-injective 2-Calabi--Yau tilted algebras

Abstract

Consider a $k$-linear Frobenius category $\mathcal{E}$ with a projective generator such that the corresponding stable category $\mathcal{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in \mathcal{C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras $\mathcal{C}(l,l)$ and $\mathcal{C}(m,m)$ are derived equivalent. Furthermore we will give a description of the two-sided tilting complex which induces this derived equivalence.

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